Intersection of a plane and cylinder

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SUMMARY

The intersection of the plane defined by the equation 3x + y + z = 1 and the cylinder described by x^2 + 2y^2 = 1 can be represented parametrically. The correct parametric equations are x = cos(t), y = sin(t)/sqrt(2), and z = -3cos(t) - (sin(t)/sqrt(2)) + 1, where t is the parameter. This representation accurately describes the curve resulting from the intersection, confirming the calculations provided by the user.

PREREQUISITES
  • Understanding of parametric equations
  • Knowledge of plane and cylinder equations in 3D space
  • Familiarity with trigonometric functions
  • Basic skills in algebraic manipulation
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  • Explore the concept of parametric curves in 3D geometry
  • Learn about the geometric interpretation of intersections between surfaces
  • Study the application of trigonometric identities in parametric equations
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Students and professionals in mathematics, physics, and engineering who are working with geometric intersections and parametric representations in three-dimensional space.

Stevecgz
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Question: Find a parametric representation for the curve resulting from the intersection of the plane 3x + y + z = 1 and the cylinder x^2 + 2y^2 = 1.

What I did:

x = cost
y = sint/sqrt(2)
z = -3cost - (sint/sqrt(2)) + 1

I think I'm doing this correctly but the answer seems too easy for this type of assignment. Hoping someone could look it over and tell me if I'm missing something. Thanks.

Steve
 
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It looks alright to me.
 
Thanks d_leet.
 

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